I'd like to shim the flat behind the recoil lug on a M70 just enough to slightly float the barrel. Do I need to put shims in the rear of the action as well to accomplish this properly or can I just shim the front? Also, what is some simple shim material that will work? Maybe plastic milk jug material?? Please advise. thanks much.

Are you having accuracy problems.

I thick you are asking for trouble.

I would believe that the action could move on the shims cracking the stock.

Why screw around.

I free float all my barrels.

Glass bed the action and the first 3 inches of the barrel in front of the Action.

Float the rest.

I never hurt the accuracy by doing so and improved it 99% of the time.

I do the same, however if you want to temporarily float the barrel yes you can put some gasket paper or index card under the action. Just under the ring but not necessary. Under the bridge is ok too. You will not crack the stock.
Many barrels will shoot better if they have upward pressure at the fore end tip; especially cheap barrels. So try that first; same way; index card. That is why all Ruger barrels use that method. Upward pressure. Necessary when they used cheap Wilson barrels.

You "can" do that......but when you tighten the action screws you are putting stress on the action, especially if it something like a mauser with all those huge cutouts.

We bed actions to eliminate those stresses. You just may negate the potential gains from the float by "warping" the action......

By shimming, as you suggest, you may not get a reliable answer to your question. By shimming the receiver off its bed, you could just be creating another problem and you'd not know if it was because the receiver was shimmed or if the barrel was 'floated'. Open the barrel channel and re-seal the wood. Then, you'll be able to decide if floating the barrel helped or not.

devere - First of all, great idea.
One of my Sako's has a factory shim made of fiber on the flat.
A piece of index card will do what you want (as dpcd suggested). Make them full width both front and rear to avoid any side to side rocking action and keep the barrel space equal. Add more as needed as I don't believe one will make much of a difference as they are not very thick.
Keep us posted.